Valerii V. Buldygin, Marina K. Runovska, “On the convergence of series of autoregressive sequences in Banach spaces”, Theory Stoch. Process., 2010, Volume 16(32), Issue 1,Pages <nobr>29

On the convergence of series of autoregressive sequences in Banach spaces

Valerii V. Buldygin, Marina K. Runovska

Department of Math. Anal. and Probab. Theory, National Technical University of Ukraine (KPI), Peremogy Ave., 37, Kyiv 03056, Ukraine

Abstract: Necessary and sufficient conditions for the almost sure convergence of a series of autoregressive sequences in separable Banach spaces are studied. As an application of the obtained results, the condition for the admissible shift of a zero-mean Gaussian Markov measure is considered.

Keywords: Autoregressive sequences, almost sure convergence of random series, summability theory, Gaussian Markov sequences, continuity and singularity of probabilistic measures.

MSC: Primary 60G50, 60G15; Secondary 40C05, 60G30

Language: English